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Pauli Center for Theoretical Studies

The Swiss National Science Foundation

ETH Zurich (Computer Science and Physics Department)

Quantum Science and Technology

CQT Singapore

QAP European Project

Sandia National Laboratories

Institute for Quantum Computing

id Quantique

Simulation of fermionic lattice models in two dimensions with tensor network algorithms

Philippe Corboz, University of Queensland

The numerical simulation of strongly correlated fermionic systems in two dimensions is one of the biggest challenges in computational physics. Borrowing ideas and tools from quantum information and computation, a new generation of simulation techniques for many-body systems, the so-called tensor network algorithms (e.g. PEPS, MERA), have been proposed in the last few years. Given e.g. a 2D lattice system governed by a local Hamiltonian H, a tensor network algorithm attempts to approximate the ground state of H by means of a (in general non-unitary) quantum circuit. The efficiency of simulations depends directly on the amount of entanglement in the ground state of H, with the success of tensor network algorithms being closely related to the so-called “area law” for entanglement entropy. By considering a quantum circuit made of fermions,  tensor network algorithms have been recently extended to fermionic systems, thereby offering a new promising way to address long standing problems in condensed matter physics, such as the Hubbard model, which is conjectured to be the key model of high-temperature superconductors. After presenting a general overview on tensor network algorithms, I will discuss the most recent developments involving the simulation of fermions.